6 21 25 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 21   c = 25

Area: T = 50.99901951359
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 11.20108183696° = 11°12'3″ = 0.19554911595 rad
Angle ∠ B = β = 42.83334280661° = 42°50' = 0.74875843497 rad
Angle ∠ C = γ = 125.9665753564° = 125°57'57″ = 2.19985171445 rad

Height: ha = 16.9976731712
Height: hb = 4.85662090606
Height: hc = 4.07992156109

Median: ma = 22.89110462845
Median: mb = 14.84108220797
Median: mc = 9.06991785736

Inradius: r = 1.96111613514
Circumradius: R = 15.44441456421

Vertex coordinates: A[25; 0] B[0; 0] C[4.4; 4.07992156109]
Centroid: CG[9.8; 1.3659738537]
Coordinates of the circumscribed circle: U[12.5; -9.07703712501]
Coordinates of the inscribed circle: I[5; 1.96111613514]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.799918163° = 168°47'57″ = 0.19554911595 rad
∠ B' = β' = 137.1676571934° = 137°10' = 0.74875843497 rad
∠ C' = γ' = 54.03442464357° = 54°2'3″ = 2.19985171445 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6 ; ; b = 21 ; ; c = 25 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 6+21+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-6)(26-21)(26-25) } ; ; T = sqrt{ 2600 } = 50.99 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50.99 }{ 6 } = 17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50.99 }{ 21 } = 4.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50.99 }{ 25 } = 4.08 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6**2-21**2-25**2 }{ 2 * 21 * 25 } ) = 11° 12'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-6**2-25**2 }{ 2 * 6 * 25 } ) = 42° 50' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-6**2-21**2 }{ 2 * 21 * 6 } ) = 125° 57'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50.99 }{ 26 } = 1.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 11° 12'3" } = 15.44 ; ;




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